Example 6.2 Consider \(X=\mathbb {R}^n\) , equipped with the usual Euclidean distance and the Lebesgue measure.
Then \(N^{1,p}(\mathbb {R}^n)=W^{1,p}(\mathbb {R}^n)\) , and \(\vert \nabla u\vert \in \mathcal {D}_p(u)\)  if
\(u\in W^{1,p}(\mathbb {R}^n)\) ; see e.g. [1]}.
